Coronaviruses are enveloped RNA viruses which show marked tissue and species tropisms. Mouse hepatitis virus (MHV) is one example of the coronaviruses. In this dissertation I will discuss two aspects of coronaviruses: 1) the RNA polymerase of the A59 strain of MHV; and 2) the role of coronavirus receptors in coronavirus species specificity. An in vitro replication system was developed to study the RNA dependent RNA polymerase of MHV-A59. Extracts of MHV-infected cells produced MHV-specific RNAs of genomic and subgenomic sizes. In vitro synthesized viral RNA became associated with the viral nucleocapsid protein to form ribonucleoprotein complexes. When cell lines of non-murine origin were inoculated with MHV, they produced no MHV RNAs or proteins. Therefore, species-specific host restriction for MHV may occur at the level of viral attachment or penetration. MHV receptors in mouse strains susceptible, semi-resistant or resistant to MHV infection were compared on hepatocyte and intestinal brush border membranes. All strains tested except the fully resistant SJL/J strain expressed a 100-120 kilodalton MHV receptor, but C57BL/ 6 mice expressed a larger receptor on the intestine. MHV3 bound to the same receptor as MHVA59 indicating that different MHV strains share a common receptor. The species specificity of the MHV receptor was also investigated. Intestinal brush border membranes from nine other species did not express any MHV binding activity. Therefore, the marked species specificity of MHV appears to be determined by absence of the MHV -specific receptor in other species. Solid phase assays to detect virus receptors on intestinal brush border membranes from normal host species were developed for canine (CCV), feline (FIPV), porcine (TGEV), human (HCV-229E), and bovine (BCV) coronaviruses. The antigenically related coronaviruses, CCV, FIPV, TGEV, and HCV-229E bound to intestinal brush border membranes of dog, cat, pig, and human.